How does the DNA sequence affect the Hill curve of transcriptional response?

The Hill coefficient is often used as a direct measure of the cooperativity of binding processes. It is an essential tool for probing properties of reactions in many biochemical systems. Here, we analyze existing experimental data and demonstrate that the Hill coefficient characterizing the binding of transcription factors to their cognate sites can in fact be larger than one-the standard indication of cooperativity-even in the absence of any standard cooperative binding mechanism. We demonstrate that this effect occurs due to the disordered binding energy of transcription factors to the DNA molecule and the steric repulsion between the different copies of the transcription factor. We show that the enhanced Hill coefficient implies a significant reduction in the number of copies of the transcription factors which is needed to occupy a cognate site and, in many cases, can explain existing estimates for number of copies of the transcription factors in cells.